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A new measure of skill for the new scoring system--the PRoot!
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skrumgaer wrote
at 1:50 PM, Sunday September 9, 2007 EDT
Under the new scoring system, the score of a player who is playing other kdicers of equal skill would follow a random walk. The average straight-line difference between a player’s score and zero will be proportional to the square root of the number of games (see Wikipedia http://en.wikipedia.org/wiki/Random_walk) for a given level of table. So I propose as a measure of a player’s current standing the player’s score divided by the square root of games played (Points/RootGamesPlayed or PRoot for short). A player with skill will tend to have an average straight-line difference from zero that is greater than average random walk.
The advantages of the PRoot are as follows: 1. It is easy to calculate. 2. It is a fair balance between rewarding games played and rewarding points per game. 3. Playing at higher level tables is rewarded. 4. Players who horse around when their scores are zero are penalized. The one disadvantage of the PRoot is: 1. Luck is not eliminated. There will be considerable variation in a player’s PRoot. To eliminate the luck factor, we would need the average of the PRoot, but the data are not available to calculate this. The following table shows the current top 25’ers, their scores, games played, percentage profiles, and PRoots. I had the take the diamonds out to convert the scores to numerical fields. I express my appreciation to mrMichaels and RedSox 5445 for comments regarding scoring. 3 rnd 761 127 25% 18% 9% 6% 6% 9% 23% 67.53 8 Yce 538 71 26% 25% 9% 11% 9% 8% 8% 63.85 2 wishbone 771 156 21% 18% 19% 12% 11% 10% 7% 61.73 11 I'm Lost 505 67 37% 20% 11% 11% 5% 7% 4% 61.70 10 petomni 520 101 22% 16% 16% 12% 9% 14% 5% 51.74 1 Vohaul 905 339 19% 12% 10% 9% 11% 15% 19% 49.15 6 Phoenix37 581 153 21% 19% 11% 11% 5% 12% 17% 46.97 4 Zosod 624 187 20% 14% 17% 11% 9% 13% 12% 45.63 13 DoobiusMalcor 457 104 27% 12% 7% 10% 13% 12% 15% 44.81 18 SodaPop 403 81 19% 20% 11% 11% 11% 14% 11% 44.78 5 ProxyCheater 583 210 17% 17% 14% 11% 10% 17% 11% 40.23 15 Danny_DCB 413 112 22% 11% 12% 13% 15% 12% 12% 39.02 23 Cleopatra 380 96 23% 13% 13% 17% 16% 5% 9% 38.78 20 pUPAS 389 110 20% 21% 11% 8% 12% 8% 16% 37.09 14 Vermont 425 141 21% 17% 9% 19% 14% 10% 7% 35.79 7 Jos�lito Michaud 580 264 16% 21% 15% 16% 9% 9% 10% 35.70 19 XxDiceyGirlxX 399 133 18% 21% 12% 13% 12% 9% 12% 34.60 9 Ssergio 522 229 23% 15% 16% 14% 12% 10% 7% 34.49 21 Whitehawk 382 163 14% 22% 10% 8% 9% 17% 15% 29.92 16 jss 413 229 17% 16% 10% 13% 12% 12% 17% 27.29 25 Kehm 372 189 16% 13% 11% 8% 14% 15% 19% 27.06 12 GronamOx 491 343 19% 15% 10% 16% 12% 12% 13% 26.51 17 fandango1 407 286 14% 15% 13% 15% 15% 13% 12% 24.07 24 sisu 375 286 16% 18% 10% 10% 11% 14% 18% 22.17 22 Polamalu 380 305 17% 12% 15% 13% 14% 14% 12% 21.76 3813 skrumgaer 0 167 12% 10% 17% 16% 16% 14% 11% 0.00 |
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Elemental wrote
at 2:59 PM, Sunday September 9, 2007 EDT This one makes more sense.
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nuflis wrote
at 5:30 PM, Sunday September 9, 2007 EDT I like this system also. But it works with a minimum sample size. 30, can be enough if we trust the Central limit theorem.
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XxDiceyGirlxX wrote
at 5:44 PM, Sunday September 9, 2007 EDT Hmmm, this makes a lot of sense.
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skrumgaer wrote
at 5:46 PM, Sunday September 9, 2007 EDT Good point, nuflis, like a batter can't count his batting average unless he has had enough times at bat.
Since there is so much variablity in the PRoot, it probably doesn't need decimals. A whole number will give us enough significant digits. |
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skrumgaer wrote
at 5:53 PM, Sunday September 9, 2007 EDT And I'm not completely satified with the designation PRoot. It might be better to call it PPRG, or Points Per Root Game, to make is analogous to PPG, Points Per Game, used in many sports.
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JDizzle787 wrote
at 8:25 PM, Sunday September 9, 2007 EDT Christ,you statisticians make me puke. Just Kidding. but really, why?
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Beals wrote
at 8:39 PM, Sunday September 9, 2007 EDT No crap. Best system is no score or rank, just win/loss percentage. I don't need a stinking score to prove myself. I just want to win first place every game, and so should anyone else. Finishing in second but "earning" five points is like winning the special olympics.
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DoobiusMalcor wrote
at 8:40 PM, Sunday September 9, 2007 EDT Central limit theorem has nothing to do with it.
I don't see the logic for rooting the denominator. If you want to avoid the aberration of small sample sizes do: TotalPoints / (GamesPlayed + 25) which merges with pure ppg with enough games. Otherwise there seems to be insufficient penalty for huge numbers of played games. |
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skrumgaer wrote
at 9:13 PM, Sunday September 9, 2007 EDT JDizzle:
Math is fun. Beals: Best system depends on the game. In NASCAR racing, all contenders are competing at once, consequences can be terrible if someone screws up "trying to win first place", and compensation (scores) are more nearly equally divided than in, say, golf. See Leeds, Von Allen, The Economics of Sports, Second Edition, Addison-Wesley. In kdice, percentage of players participating at once is tiny, so big share to the winner seems the best fit. But, unlike golf, players can interact positively or negatively. Which suggests not all share should go to the winner. Doobius: How would you compare the home run records of two hitters who have not played the same number of games, seasons, or games per season? See the comment posted by me on mrMichaels's profile page. |
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rnd wrote
at 10:30 PM, Sunday September 9, 2007 EDT finally. my vindication is complete.
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